Physica B 284}288 (2000) 1450}1451

Study of spin gap excitations in SrCu (BO ) by submillimeterwave ESR
H. Nojiri *, H. Kageyama, K. Oniduka , Y. Ueda , M. Motokawa
Institute for Materials Research, Tohoku University, Katahira 2-1-1 Aoba-ku, Sendai 980-8577, Japan
Institute of Solid State Physics, University of Tokyo, Roppongi Minato-ku, Tokyo 106-8666, JapanAbstract
Spin gap excitations have been observed directly in two-dimensional dimer system SrCu (BO ) by means of
submillimeter wave ESR. The zero-"eld energy gap shows an unexpected splitting into two branches due to theanisotropy of the inter-dimer coupling. The average coincides with the energy gap value estimated from the high "eldmagnetization process.  2000 Elsevier Science B.V. All rights reserved.
Keywords: ESR; Quantum spin system; Spin gap

A quantized plateau of magnetization in low-dimensional quantum spin system is a subject of current interest. Such plateau is expected to be realized in a systemwith localized excited states. In this case, triplets hardly
propagate in the system and thus a spin gap coexists withexcited triplets. Hence it is very interesting to observe
such localized and gapped magnetic excitations aroundmagnetization plateau. Recently, the quantized plateausof magnetization were observed for SrCu (BO ) [1].
A unique two-dimensional (2D) network of Cu> causes
a special situation, where nearest-neighbor dimers arearranged orthogonally to each other as shown schematically in the inset of Fig. 1. The theoretical investigations
have shown that the hopping of a triplet is impossible
within the "fth order in the perturbation [2]. The main
issue of the present article is the investigation of the spin
gap excitations of the system by means of ESR.
Fig. 1 shows the temperature dependence of ESR
spectra at 428.9 GHz for H""c. At low temperatures, a setof two resonance peaks marked by arrows are observed.
The temperature dependence shows that these two peaks
are the excitations from the singlet ground state. We have

* Corresponding author. Tel.: #81-22-215-2019; fax: #8122-215-2016.
E-mail address: nojiri@.imr.tohoku.ac.jp (H. Nojiri)measured the frequency dependence of these peaks up to
1 THz and found that the two peaks show a characteristic frequency dependence as schematically depicted in
the inset of Fig. 1. It clearly indicates that the two modes
correspond to the transitions between the ground singlet
state and the "rst excited triplet state. The zero-"eldenergy gaps are evaluated as 708 and 738 GHz. The
average of these two gaps are found to be 722 GHz and it
is close to the gap estimated so far by di!erent methods[1,3,4].
A possible candidate for the zero-"eld splitting between the two triplets is the "nite inter-dimer interaction
J. For "nite J, we expect the two excited states to be
separated from each other by the order of J. Since thenext-nearest neighbor coupling J is estimated to be 68
K, it is not reasonable to attribute the experimentallyobserved small splitting to the inter-dimer coupling evenif we take the signi"cant frustration e!ect into account[2]. To investigate the origin of the splitting, we measured the "eld orientation dependence of the two spin
gap excitations as shown in Fig. 2. A large anisotropy ofthe splitting is found and thus we speculate that theanisotropy of exchange interaction is the origin of thissplitting. As is well known, the anisotropic exchange iscaused by the spin-orbit coupling j and the j is also
related to the anisotropy of g-value. The angular dependence of the g-value shown in Fig. 2 indicates that a large
anisotropy exists between H""c and H""a. Thus we can

0921-4526/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 6 9 0 - 3

H. Nojiri et al. / Physica B 284}288 (2000) 1450}1451

Fig. 1. Temperature dependence of ESR spectra at 428.9 GHz.
Two arrows indicate the singlet-triplet transitions. The energy
diagram and the con"guration of two dimers in the c-plane aredepicted schematically in the inset. Open circles denotes theCu> ions.

1451

expect that the J
deviates from J , where J and??
AA
AAJ
are the components of the inter-dimer exchange??
coupling along the c-axis and a-axis, respectively. Hencethe small splitting for H""c can be attributed to the di!erence between J and J .
AA??
Finally we mention the line shape of paramagnetic
signals. Above 10 K, only one broad ESR signal can beobserved at around 13.4 T as shown in Fig. 1. The resonance "eld shows no clear temperature dependence
between 10}25 K. On the other hand, the line shapedeviates from the Lorentzian below 15 K and shows anintermediate shape between the Lorentzian and Gaussian. As is well known, such behavior appears when spin
di!usion is important in the 2D system. However, for thepresent system the line shape can be "tted by the 2D spin
di!usion theory only in a very narrow temperature
region. Moreover, at around 10 K, the signal can be "tted
as the superposition of two components with di!erent
linewidths possibly due to the existence of multiple excited states [5].

References

Fig. 2. The angular dependence of resonance "elds B of the
two singlet-triplet transitions (closed rectangles and closedcircles) and the g-value (closed triangles) in the ac-plane.

[1] H. Kageyama, K. Yoshimura, R. Stern, N.V. Mushnikov,K. Onizuka, M. Kato, K. Kosuge, C.P. Slichter, T. Goto,
Y. Ueda, Phys. Rev. Lett. 82 (1999) 3168.
[2] S. Miyahara, K. Ueda, Phys. Rev. Lett. 82 (1999) 3701.
[3] H. Kageyama, M. Nohara, H. Suzuki, K. Onizuka, Y. Ueda,
H. Takagi, Physica B, to be published.
[4] H. Kageyama, K. Onizuka, Y. Ueda, M. Nishi, N. Aso,T. Yoshihama, K. Kakurai, unpublished.
[5] H. Nojiri, H. Kageyama, K. Onizuka, Y. Ueda,
M. Motokawa, J. Phys. Soc. Japan 68 (1999) 2906.